Understanding by Design
Unit Planning Template
Unit: Number Systems and Sets
Length of Unit
Stage 1 –Desired Results
Where are we going?
NY State Standards:
7.N.1 Distinguish between the various subsets of real numbers (counting/natural
numbers, whole numbers, integers, rational numbers, and irrational numbers).
7.N.2 Recognize the difference between rational and irrational numbers (e.g., explore
different approximations of pi)
7.N.3 Place rational and irrational numbers (approximations) on a number line and
justify the placement of the decimal.
A.N.1 Identify and apply the properties of real numbers (closure, commutative,
associative, distributive, identity, inverse) Note: Students do not need to identify groups
and fields, but students should be engaged in the ideas.
A.A.29 Use set-builder notation and/or interval notation to illustrate the elements of a
set, given the elements in roster form.
A.A.30 Find the complement of a subset of a given set, within a given universe
A.A.31 Find the intersection of sets (no more than three sets) and/or union of sets (no
more than three sets)
CCSS:
N-RN.3 Explain why the sum or product of two rational numbers is rational;
that the sum of a rational number and an irrational number is irrational;
and that the product of a nonzero rational number and an irrational
number is irrational. (A.N.1)
Standards for Mathematical Practice:
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Learning Outcomes/Goals:
1. Students will be able to identify and use the various properties of real numbers
to manipulate, rewrite, or simplify algebraic and numerical expressions.
2. Students will be able to identify, distinguish, and illustrate (Venn diagrams,
various set notations) sets, subsets, and relationships between subsets
(intersection, union, complement), including the set of real numbers.
Enduring Understandings:
We will understand…
Essential Questions:
How do you create order out of chaos?
There are ways to organize, group, and
categorize things based on their characteristics.
Knowledge
We will know…
Set notations, properties of real numbers,
essential vocabulary related to sets and
real numbers
Skills
We will be able to…
Create a Venn Diagram with up to three
subsets.
Interpret sets in roster, interval, and setbuilder notation. Write sets in roster and
interval notation.
Identify which property of real numbers is
illustrated in an algebraic expression or
equation.
Place numbers expressed in various ways
correctly on a number line.
Stage 2 – Assessment Evidence
How will we know we are there?
Performance/Products Tasks:
Other Evidence:
Pre-Assessment on Venn Diagrams, Real
Numbers, Placement on Number Line
Formative assessment (informal and using
SENTEO clickers)
Quiz/Ticket Out the Door on following:
Rational vs. Irrational Numbers
Set Notations
Venn Diagrams
Set Relationships (Union,
Intersection, Complement)
Properties of Real Numbers
Bellwork problem(s) as check for
understanding
Summative Unit Test
Writing Tasks:
Create Venn Diagram and/or set notation
describing collection of their own objects.
Reading Tasks:
Stage 3 – Learning Plan
How will we get there?
Individual Lesson Plans with Resources
Set of Real Numbers (Day 1)
Properties of Real Numbers (Days 2 & 3)
Introduce Sets and Set Relationships using Roster Notations (Day 4 & 5)
Other Set Notations (Day 6)
Real World Applications of Sets (Day 7)